I've been carrying an SLR around the parks for years.
I started with my Canon Rebel G and Sigma 28-200 lens, then later added a Canon Speedlite 220EX flash unit.
Now I carry my Canon Digital Rebel 300D with my Kelly lens (Sigma 18-125), and I still carry the Speedlite:
Carrying a large camera around the parks is not that big a deal when you consider how much better your pics will be, but it does require a few preparations.
1) A REALLY good camera strap. For many years I used a 2" cotton web strap. Recently I switched to an x-harness that is much more comfortable. Use the wrong strap, and the weight of your camera will give you pains in your neck or shoulders in a few hours.
2) Get a walkaround lens. Unless you feel like lugging one or two spare lenses around all day, and switching off constantly (thus missing a shot or two when quickness is required), you need a lens with a good range of zoom from wide to tele. I like the Sigma 18-125, known here as the Kelly because of Kelly Grannell's enthusiastic endoresment of it (I second the emotion every time she does that, by the way).
3) Figure out a comfortable amount of extra equipment to carry with you. You may not need 3 extra batteries, 6 memory cards, and a cleaning kit - or you might. Each person's shooting style is a little different. I carry 1 or 2 extra memory cards, my flash, a pocket-size tripod, and a 1-gallon Ziploc bag that I use as a
Camera Poncho
4) Use it! Instead of lugging the camera around all day and only taking 1 pic per hour, take a bunch of pics. Use the shotgun approach; snap at everything, you can always delete the bad pics later.